Dame Clara Furse, a former chief executive of the London Stock Exchange, has been warned that she might not get the full backing of MPs for her nomination to the new Bank of England committee set up to look for the next bombs in the financial system.

Under fire over a previous role on the board of the bailed-out bank and insurance group Fortis, Furse was giving evidence to the Treasury select committee (TSC) in a pre-appointment hearing on Tuesday. Others facing MPs were a former Barclays boss, Martin Taylor, and ex-Goldman Sachs banker, Richard Sharp, who are joining the financial policy committee (FPC).

Tory MP Jesse Norman told Furse her evidence, which began with a discussion about whether the FPC needed extra powers to limit the leverage ratio of banks, was unimpressive. Norman said: "I want to say I shall be thinking very seriously about whether I can support this nomination."

The TSC will announce in the next 48 hours its verdict on the three new members of the FPC, which is due to hold its next quarterly meeting this month.

Taylor surprised MPs when he said there had been a period of "less bad" rigging of Libor during the 2008 financial crisis, while Sharp was asked whether his donations to the Conservative party could compromise his independence on the FPC.

Furse drew criticism after insisting she had not seen reports that the independence of the new appointees was being questioned and that she did not support an immediate new power to impose limits on the leverage banks could take.

She was a Fortis non-executive director and on the risk and capital committees when the Dutch-Belgian firm was involved in taking over ABN Amro, along with Royal Bank of Scotland and Santander, during the 2007 credit crunch.

Fortis needed a bailout, as did RBS. Furse said she deeply regretted the losses to shareholders, but that taxpayers in the Netherlands, Belgium and Luxembourg had not done too badly from the rescue. She insisted the deal had floundered because of execution risk and not because of the quality of the assets and that legal advice taken by Fortis had prevented the firm from pulling out of the deal.

Furse, the first female member of the FPC, said her "searing" experience on the Fortis board was relevant as it "sensitised me to all kinds of extreme risks".

George Mudie, a Labour member of the committee, asked Sharp whether his initial FPC interview with Lady Hogg, an adviser to former Conservative chancellors and wife of former cabinet minister Douglas Hogg, had compromised his appointment as he was a Tory party donor. Sharp insisted this was not the case.

Taylor, who quit as chief executive of Barclays in 1998, was questioned about his role as an adviser to Goldman Sachs until 2005. Asked about the Libor rigging, which forced out one of his successors, Bob Diamond, Taylor said there had been episodes of less bad rigging of the key rate. This was when low rates were submitted during the financial crisis, rather than when the rate was rigged to make profits for banks.

"Libor rates were invented. Putting a rate a little bit lower was a sensible thing to do. We need to keep in perspective how dangerous [a period] it was," said Taylor. "I can't get excited about what seems to have been a help to financial stability."

A former member of the Independent Commission on Banking, Taylor said he supported the drive by regulators to require banks to hold more capital. "Bigger banks aren't going to lend until their capital positions have been repaired," he said.

Sharp and Taylor insisted the regulator had not been soft on Lloyds Banking Group and Royal Bank of Scotland by not forcing them to raise new capital from shareholders. Taylor said they were "making violent changes to their business plans".